On Empyrea, McCoy discovers Anna, a daughter he never knew he had. McCoy soon realizes that the isolationalist Empyreans must not learn her father is an off-worlder, and that her genes are less than "perfect". As relations with the Empyreans collapse around him, McCoy must find a way to save his newfound daughter from the harshest penalty her planet can impose!

The Enterprise has been placed at the disposal of Ambassador Mark Rousseau, a former friend of McCoy's. When Rousseau was captain of the USS Feynman and McCoy his chief medical officer, they made contact with a human colony on Nova Empyrea that had deliberately isolated itself a hundred and fifty years earlier to practise genetic engineering. The Empyreans agreed to the Federation establishing an observatory on the planet to study its unusual star system but now many want it removed. They have agreed to let the Federation negotiate a renewal of the treaty on condition McCoy and Rousseau are the negotiators.

The two men meet with the planet's president, Elizabeth March, an old acquaintance. Privately, she tells McCoy that he is the father of her daughter Anna. When Anna turns eighteen, she will be expected to undergo a medical for a reproduction license, which will expose the genetic fraud. Elizabeth wants McCoy to take her away from the planet but Anna wants to remain so he instead works on a way to fool the genetic test. In the process, he learns that he is not her father: Rousseau is.

Anna chooses to undergo the risky medical procedure over her mother's objections. However, Ethan, a youth in love with Anna, takes McCoy hostage to try and force the Enterprise to take him and Anna and others who oppose their world's isolation off planet. In their absence, Anna's treatment starts to fail and Ethan releases McCoy in order to save her.

Meanwhile, Spock and Scotty have been working with Doctor Ortega, an Empyrean scientist who approves of strict segregation, to keep the observatory in working order. They eventually realise that someone has sabotaged the facility, creating a series of failures that threaten to release radiation. Spock and Scotty manage to beam the reactor core aboard the Enterprise, safely shutting it down.

With Ortega now speaking in favour of contact with the outside universe, the Empyreans narrowly vote in favour of renewing the treaty. It is hoped this will be the first step in establishing further involvement in galactic affairs, with Anna volunteered to travel to Earth aboard the Enterprise.